The novel is set in and reflects the mores and technology of a small town in New England in the early 1960s, the time when the book was written. There are no personal computers, no microwaves, and no cell phones. A radio issues hurricane warnings. We learn that Meg and her mother struggle with Meg's hair, having trouble "putting it up," which would mean using pin curls or curlers, something we seldom, if ever, do today.

When the children arrive at Camazotz, the neighborhood is described as a typical 1950s housing development and acts as a commentary on the "conformity" people worried about in that period, when modern identical subdivisions of the Levittown variety had only been built for about fifteen years. We learn that:

The houses in the outskirts were all exactly alike, small square boxes painted gray. Each had a small, rectangular plot of lawn in front, with a straight line of dull-looking flowers edging the path to the door.

The children on Camazotz deliver newspapers on bicycles, bounce balls, and skip ropes, all activities we associate with bygone eras. 

The book thus is both science fiction, complete with interstellar travel and alien beings, and a period piece reflecting white middle-class life in an era roughly 55 years past.

A Wrinkle in Time is the first book in a series written by Madeleine L'Engle. The books are written for children but have a timeless appeal because of their characters, their universal themes, and their science fiction elements. 

Time is very important in many science fiction stories, as they are often set in a time other than the present; however, in A Wrinkle in Time (despite the reference in the title), the time period does not matter. What matters more is place in time, as the characters move back and forth in space more than time. The entire story explores the idea that “a straight line is not the shortest distance between two points.” 

The best way to characterize the time period of this novel is to say it is set in the present. At the time it was written, the present was the early 1960s, and that seems consistent with the everyday lives of the Murray family (such as what they eat and drink and what they wear).

What is the literary time period for A Wrinkle in Time by Madeline L'Engle?

This is a tough question because scholars (and literature texts) often disagree on this. While some scholars think the literary period in American Literature here is as general as saying it is part of "literature after 1861," other texts will insist that it is a part of Contemporary American Literature. I am of the latter school. Therefore, I put forth that A Wrinkle in Time, considering its first publication date of 1963, is a piece of Contemporary American Literature. I want to go further, however, and mention another irony, which is that A Wrinkle in Time is often placed within two different genres as well: the young adult novel and the science fantasy. The first of the two genres refers to the general age of the audience for which the novel was written. The second of the two genres refers to the content of fantasy mixed with science. Th eNotes guide to the novel also mentions that it is a "fast-paced adventure tale."